title: Permutation method for evaluating topographic craniofacial correlations.
abstract: BACKGROUND
  Correlations between cephalometric measurements are frequently assumed to represent biologic associations. However, a significant portion of such correlations might arise from purely geometric dependencies, when measurements share common landmarks. Analytic calculation of this topographic component is difficult. The purpose of this study was to propose a permutation method for evaluating the topographic component of cephalometric correlations.
  
  
  METHODS
  The method consisted of creating a virtual sample of cephalometric tracings (landmark configurations) from the original biologic sample under investigation. Each novel landmark configuration was constructed by assigning coordinates to the cephalometric points; the coordinates of each point were taken randomly from the original sample, each from a potentially different subject. Correlation analysis was performed separately on both samples and the results compared. Biologic meaning was ascribed only when there was a significant difference in correlation values between the samples. Confidence intervals for assessing statistical significance were calculated by using a randomization approach. The method was tested on a sample of 170 radiographs to evaluate the correlation between cranial base angle (NSBa) and angles SNA and SNB, as well as between ANB angle and the Wits appraisal.
  
  
  RESULTS
  No biologic association was found between ANB and Wits, or between NSBa and SNA. The biologic correlation between NSBa and SNB was statistically significant but low (r(2) = 12%).
  
  
  CONCLUSIONS
  Topographic associations between cephalometric measurements are ubiquitous and difficult to assess. The proposed method enables evaluation of their relative strength without the need for analytic solutions.
authors.affiliation: Orthodontic Department, University of Athens, School of Dentistry, Athens, Greece. dhal@dhal.com
authors.forename: Demetrios J
authors.initials: DJ
authors.lastname: Halazonetis
mesh_terms: D000293:Adolescent; D001695:Biology / Q000706:statistics & numerical data; D002508:Cephalometry / Q000706:statistics & numerical data*; D002648:Child; D005145:Face / Q000033:anatomy & histology* / Q000000981:diagnostic imaging; D005260:Female; D006801:Humans; D008297:Male; D008334:Mandible / Q000033:anatomy & histology / Q000000981:diagnostic imaging; D008437:Maxilla / Q000033:anatomy & histology / Q000000981:diagnostic imaging; D015233:Models, Statistical; D009295:Nasal Bone / Q000033:anatomy & histology / Q000000981:diagnostic imaging; D011859:Radiography; D012658:Sella Turcica / Q000033:anatomy & histology / Q000000981:diagnostic imaging; D012886:Skull / Q000033:anatomy & histology* / Q000000981:diagnostic imaging; D019291:Skull Base / Q000033:anatomy & histology / Q000000981:diagnostic imaging; D014584:User-Computer Interface